It is known to use a navigation apparatus of a vehicle to display not only a route to the destination but also an estimated time of arrival. It is also known that an earlier time of arrival cannot be reconciled with a low fuel consumption, in which case there is an exchange relationship between these two variables since a low fuel consumption is to the detriment of an early time of arrival and an early time of arrival is associated with an increased fuel consumption related to the resulting accelerations associated therewith. It is recognized that the fuel consumption and the complementary variable of the time of arrival (or the driving time linked thereto) depend not only on the driving style and the loads which are switched on in the vehicle, but also on the traffic and road conditions, with the result that the variables of the fuel consumption and time of arrival can be recorded only with restricted precision using methods which do not take this into account.